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Unit 10: Time Series

show that, in general, these magnitudes have been rising over a fairly long period. As opposed Notes
to this, a time series may also reveal a declining trend, e.g., in the case of substitution of one
commodity by another, the demand of the substituted commodity would reveal a declining
trend such as the demand for cotton clothes, demand for coarse grains like bajra, jowar, etc. With
the improved medical facilities, the death rate is likely to show a declining trend, etc. The
change in trend, in either case, is attributable to the fundamental forces such as changes in
population, technology, composition of production, etc.
According to A.E. Waugh, secular trend is, “that irreversible movement which continues, in
general, in the same direction for a considerable period of time”. There are two parts of this
definition: (i) movement in same direction, which implies that if the values are increasing (or
decreasing) in successive periods, the tendency continues; and (ii) a considerable period of time.

Notes There is no specific period which can be called as a long period. Long periods are
different for different situations. For example, in cases of population or output trends, the
long period could be 10 years while it could be a month for the daily demand trend of
vegetables. It should, however, be noted that longer is the period the more significant
would be the trend. Further, it is not necessary that the increase or decrease of values must
continue in the same direction for the entire period. The data may first show a rising (or
falling) trend and subsequently a falling (or rising) trend.

Objectives of Measuring Trend

There are four main objectives of measuring trend of a time series data:
1. To study past growth or decline of the series. On ignoring the short term fluctuations,
trend describes the basic growth or decline tendency of the data.
2. Assuming that the same behaviour would continue in future also, the trend curve can be
projected into future for forecasting.
3. In order to analyse the influence of other factors, the trend may first be measured and then
eliminated from the observed values.
4. Trend values of two or more time series can be used for their comparison.

10.2.2 Periodic Variations

These variations, also known as oscillatory movements, repeat themselves after a regular interval
of time. This time interval is known as the period of oscillation. These oscillations are shown in
the following Figure:

Figure 10.3

Boom
Recovery

Rec ession
Depression
Period of oscillation

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